The strong CP problem is a compelling motivation for the existence of as-yet-undiscovered additions to the Standard Model of particle physics. An extraordinary cancellation between two apparently unrelated parameters in the Standard Model endows the neutron with an essentially symmetric distribution of electric charge, implying that quantum chromodynamics (QCD) conserves parity and time reversal symmetries P and CP, despite the fact that both are broken by electroweak interactions.
Axion models provide a popular explanation to this puzzle of the Standard Model, by dynamically restoring CP as a symmetry of the QCD vacuum. Yet in the context of a high-energy theory with broken global symmetries, which encodes for example the expected effects from quantum gravity, simple axion models require their own severe form of fine-tuned cancellations to prevent unacceptably large violations of CP symmetry in the vacuum.
Constructing a model that safeguards the axion against these catastrophic effects is highly nontrivial, and has been an active area of research from around 1990 to the present. Typical solutions in the literature invoke intricate structures of new symmetries and particles, leading an ongoing search for simpler and more aesthetically pleasing models.
This thesis explores some supersymmetric models proposed by the author as new, robust solutions to the strong CP problem. In particular, the composite axion model of  provides a compellingly simple extension to the MSSM, with built-in B − L symmetry, a naturally O(TeV) scale for electroweak physics, and sufficient protection from symmetry-violating effects for the axion model in the preferred window of parameter space, where the axion is a viable candidate for dark matter.